What's causing front-end shake?

Dear Tom and Ray: About three weeks ago, I was pulling into a parking space, and just before stopping I heard and felt what appeared to be a large impact. There was no one around and nothing to hit. I walked around the car and looked under it, but I could see no problems. Today I was pulling into a parking space and heard and felt what appeared to be an impact from another car. There were no cars around, nor objects that I could have hit. I did a walk around, but I could find nothing wrong. Both times, my dogs were in the car, and both times they became agitated. I have tried to reproduce the effect, but could not. If it had happened once, I could ignore it, but twice suggests that it will happen again. The next time, it could be at a higher speed. The first time, I was within a few feet from stopping, and I had just turned to the left. The second time, I was a few feet from stopping, and I was turning to the right. The only thing the two incidents had in common was that I was nearly stopped. My limited knowledge of cars leaves me puzzled. Can you help? — Bob
Ray: Our limited knowledge of cars often leaves us puzzled, too, Bob.
Tom: We should start by saying that we don't know what's wrong with your car. We'll give you some ideas, but this is something that a mechanic is going to have to find for you using his eyes, ears, hands and tuchus.
Ray: Whenever there are strange noises or, more importantly, shaking coming from the front end, there's one thing we always check first ...
Tom: Whether the customer is up to date on his liability insurance premiums.

Ray: Right. Because shaking and quaking from the front end can mean that an important piece of your front suspension or steering assembly is worn out, which means a wheel could fall off. You don't tell us the age of your car, Bob. But obviously, as a car gets older, chances of this sort of catastrophic failure go up.
Tom: So ask a mechanic you trust to take a thorough look at the front end. Make sure your ball joints, wheel bearings and control arms, etc., are all in good shape and still firmly attached to the car.
Ray: If they are, my first guess would be that you have a front axle that's binding up. That tends to happen when you make the sharpest turns — like when parking.
Tom: The next thing I'd look at would be your motor mounts. If you have a broken motor mount or two, your engine and transmission literally can jump around inside the engine compartment. And under certain circumstances, it could create jolting sensations as it jumps into or out of position.
Ray: You also could have a brake that's sticking. You're obviously using the brakes when you park, and if one of the calipers gets stuck, it could jolt the car when it gets unstuck.
Tom: The final thing to suspect would be the transmission. It could be something as simple as a rough downshift into first gear that you're feeling. But it would have to be awfully rough to do what you describe. And I can't explain why it would happen only when you're parking.
Ray: So those are the things to start with, Bob. Get the potentially deadly stuff checked out first, and then move on to the merely obscenely expensive stuff. Good luck!

(Car Talk is a nationally syndicated column by automotive experts (and brothers) Tom and Ray Magliozzi. Write to them at the Car Talk website.)